Leading logarithmic corrections and uncertainty of Muonium hyperfine splitting calculations

Karshenboim, Savely G.

doi:10.1007/bf01437414

Cited by 37 publications

(41 citation statements)

References 36 publications

(35 reference statements)

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“…In view of the complexity of the numerical calculations an independent consideration of this correction would be helpful. Lepage(1994) [254], [118] The very presence of the recoil factor m/M emphasizes that the external field approach is inadequate for calculation of recoil corrections and, in principle, one needs the complete machinery of the two-particle equation in this case. However, many results may be understood without a cumbersome formalism.…”

Section: Nonlogarithmic Contributions Of Order α(Zα) 3 E F and Of Higmentioning

confidence: 99%

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Theory of light hydrogenlike atoms

2001

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The present status and recent developments in the theory of light hydrogenic atoms, electronic and muonic, are extensively reviewed. The discussion is based on the quantum field theoretical approach to loosely bound composite systems. The basics of the quantum field theoretical approach, which provide the framework needed for a systematic derivation of all higher order corrections to the energy levels, are briefly discussed. The main physical ideas behind the derivation of all binding, recoil, radiative, radiative-recoil, and nonelectromagnetic spin-dependent and spin-independent corrections to energy levels of hydrogenic atoms are discussed and, wherever possible, the fundamental elements of the derivations of these corrections are provided. The emphasis is on new theoretical results which were not available in earlier reviews. An up-to-date set of all theoretical contributions to the energy levels is contained in the paper. The status of modern theory is tested by comparing the theoretical results for the energy levels with the most precise experimental results for the Lamb shifts and gross structure intervals in hydrogen, deuterium, and helium ion He + , and with the experimental data on the hyperfine splitting in muonium, hydrogen and deuterium. *

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Section: Nonlogarithmic Contributions Of Order α(Zα) 3 E F and Of Higmentioning

confidence: 99%

“…(318) and the leading logarithmic Dirac correction to the Coulomb-Schrödinger wave function [243,18,118] (see Fig. 84)…”

Section: Recoil Corrections Of Relative Order (Zα)mentioning

confidence: 99%

Theory of light hydrogenlike atoms

2001

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“…However, if the leading and the next-to-the leading terms are of the same sign, we estimate the uncertainty as a half value of the whole logarithmic contribution (cf. 59,13,16 ). Thus, a calculation of the next-to-leading terms does not reduce an uncertainty.…”

Section: Higher-order Logarithmic Corrections and Uncertainty Of Posimentioning

confidence: 99%

Precision Study of Positronium: Testing Bound State Qed Theory

Karshenboim

2004

Int. J. Mod. Phys. A

118

109

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As an unstable light pure leptonic system, positronium is a very specific probe atom to test bound state QED. In contrast to ordinary QED for free leptons, the bound state QED theory is not so well understood and bound state approaches deserve highly accurate tests. We present a brief overview of precision studies of positronium paying special attention to uncertainties of theory as well as comparison of theory and experiment. We also consider in detail advantages and disadvantages of positronium tests compared to other QED experiments.

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“…Those operators do not contribute into logarithmic corrections to ground state hyperfine structure [32,31] and were not considered in Ref. [27].…”

Section: Finally One Can Obtainmentioning

confidence: 99%

“…[34] (see also Refs. [37,32,18]) and we follow consideration there. The hadronic contribution is taken from Ref.…”

Section: Finally One Can Obtainmentioning

confidence: 99%

Hyperfine structure of the ground and first excited states in light hydrogen-like atoms and high-precision tests of QED

Karshenboim

Иванов

2002

Eur. Phys. J. D.

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Abstract. We consider hyperfine splitting of 1s and, in part, of 2s levels in light hydrogen-like atoms: hydrogen, deuterium, tritium, helium-3 ion, muonium and positronium. We discuss present status of precision theory and experiment for the hfs intervals. We pay a special attention to a specific difference, D21 = 8E hfs (2s) − E hfs (1s), which is known experimentally for hydrogen, deuterium and 3 He + ion. The difference is weakly affected by the effects of the nuclear structure and thus may be calculated with a high accuracy. We complete a calculation of the fourth order QED contributions to this difference and present here new results on corrections due to the nuclear effects. Our theoretical predictions appear to be in a fair agreement with available experimental data. Comparison of the experimental data with our examination of D21 allows to test the state-dependent sector of theory of the hfs separation of the 1s and 2s levels in the light hydrogen-like atoms up to 10 −8 . PACS

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Leading logarithmic corrections and uncertainty of Muonium hyperfine splitting calculations

Abstract: Abstract. Leading logarithmic corrections into hyperfine splitting of the Muonium ground state are evaluated. A new term in the order c~(Zc03 ln(ZcOvv is obtained. A status of theoretical calculations of the HFS is observed and main items of theoretical uncertainty are considered.

Cited by 37 publications

References 36 publications

Theory of light hydrogenlike atoms

Theory of light hydrogenlike atoms

Precision Study of Positronium: Testing Bound State Qed Theory

Hyperfine structure of the ground and first excited states in light hydrogen-like atoms and high-precision tests of QED

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